Via "n??" I looked at the code. There is a line
prec = int((digits+1) * 3.32192) + 1
where the 3.32… is an approximation to log_2(10). I highly suspect that's 
the source of it. Make the trailing 2 a 3 and it should give you more than 
the requested number of digits.

sage: n(log(10,2), prec=100)
3.3219280948873623478703194295…

H

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